1. Field of Invention
The present invention relates to a method and apparatus for making interferometric measurements, and in particular relates to a method and apparatus for making interferometric measurements with reduced sensitivity to vibration.
2. Description of Related Art
Phase shifting interferometry (PSI) has become widely used and accepted as a fast and accurate non-contact metrology tool. The underlying measurement principle of PSI is to determine the phase of the intensity signal (interference data) received at each pixel of an imaging device, and to use the phase value for each pixel to determine a height value for each pixel. A primary advantage of PSI is its high precision. With careful control of environmental conditions, measurement precision to the nanometer scale or below is possible with PSI.
However, one of the most serious impediments to wider use and improved precision of PSI is its sensitivity to external vibrations with the consequence that PSI has rarely been used in a manufacturing environment in-situ. Instead, PSI has been relegated to use during post-manufacturing inspection.
Although numerous PSI algorithms exist for analyzing interferometric data, all standard PSI algorithms generally exhibit the following two vibration sensitivity characteristics. First, most PSI algorithms experience a peak in vibration sensitivity where the vibration frequency is equal to one-half the data acquisition rate. Thus, for example, if an interferometric system acquires interference data at a rate of 30 Hz, then the interferometric system is particularly sensitive to vibrations having a frequency of 15 Hz. The reason for the peak in vibration sensitivity at one-half the data acquisition rate is that vibrations at this frequency produce phase variations which are indistinguishable from phase variations produced by surface features.
Second, for all standard PSI algorithms, the rms averaged magnitude of the vibration sensitivity at the peak is approximately equal to one-half the vibration magnitude. Thus, if the vibration has a magnitude of about one hundred angstroms, the error component of the PSI measurement may be as much as fifty angstroms, depending on the vibration frequency.
In practice, these vibration characteristics are very problematic. The data acquisition rates which are used are typically 30 to 60 Hz; thus relatively low-frequency vibrations at 15 to 30 Hz and lower cause a majority of the problems. However, vibration sources at these lower frequencies are relatively common. For example, electric motors typically operate at 60 Hz and have subharmonics at 30 Hz and 15 Hz. Thus, the peak of vibration sensitivity occurs where, in practice, there is a disproportionate amount of vibration.
Additionally, at frequencies below one-half the data acquisition rate, vibrations are still very problematic even in the absence of a peak in vibration sensitivity. This is because vibration magnitude tends to be inversely proportional to vibration frequency. That is, lower frequency vibrations tend to have a larger magnitude than higher frequency vibrations. Thus, even though sensitivity to vibration is reduced at frequencies below one-half the data acquisition rate, the vibration magnitude is increased so that the net effect is that vibration is still very much of a problem.
Various mechanical systems have been devised for active vibration compensation. However, these systems are expensive and compensate for only a limited vibration amplitude range. Other mechanical systems have been provided for passive vibration isolation. However, these systems do not effectively isolate vibrations which occur at lower frequencies. In short, therefore, mechanical systems alone have not adequately addressed the problem of PSI vibration sensitivity.
As a result, various attempts have been made to provide PSI algorithms and acquisition methods which are less sensitive to vibration. For example, a brute force approach to reducing vibration sensitivity is to use a high speed camera to acquire interference data very rapidly. While significant reductions in vibration sensitivity can be achieved using this approach, this approach is expensive to implement due to the requirement of a relatively expensive high speed camera.
According to another approach, known in the art as the "Two Camera" method and disclosed in U.S. Pat No. 5,589,938 to L. Deck, a common low speed, high density camera and a high speed, low density camera are utilized in tandem to produce measurements with both high density and reduced sensitivity to vibration. However, the requirement of two cameras makes the system difficult to implement. Additionally, the degree of computation required to combine the data from the two separate cameras is substantially more than the degree of computation required to implement standard phase extraction algorithms. As a result, throughput is decreased. Finally, the light intensity generated by the illumination source must be shared by the two cameras; thus, each camera experiences a reduction in available intensity. Since available intensity is limited, even for the most expensive illumination sources, a reduction in intensity is undesirable.
According to another approach, known in the art as "simultaneous phase quadrature", the results of two PSI channels that acquire interference data simultaneously in phase quadrature are averaged to exactly cancel ripple errors. This approach uses the fact that phase measurement errors due to vibration typically manifest themselves as a periodic deformation, or ripple, at twice the frequency of the interference signal, and the fact that the sign of the ripple error changes every .pi./2. Because of these properties, the data from the two separate PSI channels can be averaged to exactly cancel ripple errors. This concept is simple in principle, but is difficult to implement in practice. Instruments capable of simultaneous phase quadrature are highly specialized and, in most cases, are prohibitively expensive.
Although truly simultaneous phase quadrature is a significant technical challenge, it has been shown that it is possible to approach this ideal using a single PSI channel and a camera with an interline transfer architecture. (See Wizinowich, "Phase shifting interferometry in the presence of vibration: a new approach and system," Appl. Opt. 29, 3271 (1990).) According to this approach, known in the art as the "2+1" method, an interline transfer camera is used for fast acquisition of two interferograms very closely spaced in time. The gap between the two interferograms is only microseconds since they are acquired on either side of the interline transfer event between two camera frames. A reference phase shifter is adjusted so that the phase difference between these two paired interferograms is 90 degrees (i.e., the paired interferograms are in phase quadrature). The quadrature pair acquisition is followed by a third acquisition (an integration over 2 .pi. performed later) to determine the DC term of the interference pattern. Using the pair of interferograms and the DC term, the interferometric phase is calculated. The 2+1 method has demonstrably improved resistance to vibration over conventional PSI because the fact that the paired interferograms are acquired very rapidly "freezes" the vibrational state and reduces its influence on phase calculations.
Nevertheless, the requirement to separately measure the DC term by performing a 2 .pi. integration undermines the utility of the 2+1 method. The problem with obtaining the DC term in the manner described is that it limits the dynamic range of the quadrature frames in order to ensure that the DC integration does not saturate the imaging device. It also requires near-perfect ramp control and very little vibration so that integration occurs over exactly 2 .pi.. Because of these problems, the 2+1 method is difficult to implement practically and tends to perform poorly due to errors in the determination of the DC term. Finally, another problem with the 2+1 method is that the small number of data frames makes it susceptible to other forms of error, such as phase-shifter nonlinearity and miscalibration.
Other attempts at solving these problems have also not been completely satisfactory because they are expensive, difficult to implement, computationally intensive, and/or suffer increased sensitivity to other types of errors. Such approaches include, for example, those described in P. de Groot, "Vibration in phase shifting interferometry", J. Opt. Soc. Am. A 12, 354-365 (1995); C. T. Farrell and M. A. Player, "Phase-step insensitive algorithms for phase-shifting interferometry", Meas. Sci. Tech. 5, 648-652 (1994); I. Kong and S. Kim, "General algorithm of phase-shifting interferometry by iterative least-squares fitting", Opt. Eng. 34, 183-188 (1995); J. L. Seligson, C. A. Callari, J. E. Greivenkamp, and J. W. Ward "Stability of a lateral-shearing heterodyne Twyman-Green interferometer", Opt. Eng. 23, 353-356 (1984); J. A. Meiling, "Interferometric Metrology of Surface Finish Below 1 Angstrom RMS", (appearing in the April 1992 proceedings of the ASPE spring topical meeting on precision interferometric metrology); R. Smythe and R. Moore, "Instantaneous phase measuring interferometry", Opt. Eng. 23, 361-364 (1984); and U.S. Pat. Nos. 4,653,921 and 4,624,569 to Kwon and U.S. Pat. No. 5,410,405, to Schultz et. al.